Posted
by
Soulskill
on Wednesday July 31, 2013 @05:04AM
from the readers-shouldn't-be-distracted-from-drooling-on-their-shoes dept.

raque writes "The NY Times recently published two op-eds in their Philosophy section, The Stone, discussing how Heisenberg's Uncertainty principle is abused. The second is a followup to the first. The author struggled to make clear his point and left the impression he was creating a strawman argument. In his followup he said he was avoiding equations because he was writing for a general audience. I replied to both articles, asking whether showing some basic equations would have worked better, allowing math to illustrate where metaphors struggled. Now I'm asking the same question to everyone on Slashdot. Would Dr. Callendar have been better off just diving in and dealing with Heisenberg and quantum mechanics using the tools that were developed for it?"

Haha yes, of course people who are never exposed to equations are rubbish at reading them. It's a self-reinforcing feedback loop. I fear that the only way to get the general public to become more familiar with how to read equations would be to sneak them into sports coverage or something. Other than that my only other thought on the subject, is that surely anyone even a little bit interested in the Heisenberg uncertainty principle would be prepared to at least attempt equations and if not merely skim them and come back to them if needed?

It might be useful in some areas, but quantum mechanics... is one of the hardest places to start.

To put it another way, even if you introduce some equations for quantum mechanics, you are still going to look like an idiot compared to someone from the field... even someone from the field as it existed in the 1920s.

It might be better to go find experts in the field, and have them write short articles for the general public that are about established but not widely known things.

It might be better to go find experts in the field, and have them write short articles for the general public that are about established but not widely known things.

I'm not convinced. In principle it sounds great, but in practice you'll have a lot of resistance coming from several different groups:

)1) Christian fundamentalists who have no room for uncertainty in their model of the universe. To them, you might as well be reading from the Necronomicon, because anything that's unknown can't be declared true, anything that isn't true must be a lie, and all lies come from Satan.

2) New age crystal wavers who are still convinced that quantum mechanics proves there are man

I don't agree. People that read the NYT or other newspapers are not idiots. They have presumably attended school up to 12th grade and maybe even college. They should have as part of their general culture at least a "basic" understanding of maths.

I think the parent referred to the fact that in Quantum Mechanics you can have the equations right and still talk nonsense. The point is that the equations alone don't say much. This is especially true for the uncertainty relation. For example, the position-momentum

The big problem here is that those who write well usually aren't good at math, and those good at math usually aren't that good with non-math written communication. You'll probably find few people skilled in both. Perhaps the scientist should write it up with the help of a professional editor. But at any rate, why NOT add the math? Those who can't understand the math can look it up or ignore it, those who are more numerate can gain insight they wouldn't get from mere words.

Or, besides writing down the equation, EXPLAIN the equation. And not just write down what the equation says, but what it means.

Let's take a simple one - E=mc^2.

It says the amount of energy something contains is related to its mass (or the amount of "stuff") it contains. The relation is a big one - it's equal to the speed of light squared, so a tiny amount of mass (stuff) produces a LOT of energy. This equation is fundamental to nuclear physics, including peaceful uses such as nuclear power plants, to destructive uses such as nuclear weapons.

Thus the paragraph put close to the equation helps those who can't read the equation to still understand what it says, and it also explains where it's used and what it means.

But you're correct on the fundamental problem - it's because those in the sciences (and engineering) put little weight on the "arts" side of things (including things like writing) as they believe that stuff is a lot of fluff. (I can't generalize this, but if you ask a lot of people in IT, they seem to look down on studying anything that isn't related to their field - like why should a computer scientist or engineer take courses in philosophy or logic, or take classes in English or writing or even home economics).

Likewise, a lot of people take arts because they want to avoid the math and science.

Which is terrible - and it leads to this gulf of communications problems where journalists (or any writer, really) misinterprets some scientific or technical thing because the writer and the technical person are failing to communicate effectively (a problem on BOTH sides). Or how technical people look upon sales, marketing and PR people with disdain, because those people know how to relate to the public, but often fail to relate to the technical staff.

Perhaps instead of the token math or science class for an arts degree, or the token arts/business class for a technical/science degree, the two should be combined more tightly to produce a more well-rounded person who may be technical, but understands the other side.

Equations are one piece of the puzzle. Words are another piece. Pictures or examples are a third. Using one of the pieces alone may not be enough; using two or all three, if done well, could be better.

For instance, in explaining E = mc^2 you could explain it in words: the amount of energy that would be released if a small piece of matter, say 1 gram, is enormous. Or you could give the exact amount of energy produced. Or you could show a collection of Olympic size swimming pools and indicate by how much it w

I would generally agree; but generally don't go beyond linear algebra; and in the wonderful modern age add a link or a QR on a printed article with links to improve understanding.

On these extra information sites have further links to more detailed information for those that are interested, further to this the same technique could be used with any technically dense subject matter...main artcle with basic scientific info ->link-> more in depth about original content ->link-> specific detail about relevant fields

I would be opposed to any sort of calculus in an equation for popular press. But algebra? Yes. Algebra makes some things easier to understand.

And YES, it will require a little more mental effort for most people, but mental effort is a good gauge of how much someone is learning. In fact, put both the equation and a sentence explaining it. But algebra is sufficient for explaining the vast majority of physical concepts in a compact form.

Math equations are a language. A language we are all taught from middle school. We can and should use it, and use it clearly.

I fear that the only way to get the general public to become more familiar with how to read equations would be to sneak them into sports coverage or something.

Brother, that's the truth. I've got a friend, teaches business statistics to undergrads, and is always surprised when one of her students, who are mostly dim on the subject, start spewing complicated statistical concepts that they picked up on sports radio, making the connection to stats more generally.

And that says more about our teaching abilities than our learning capabilities. The students are not necessarily dim, but they're not interested in the subject without an application they're also interested in. That's why a tutor is often able to help these people when a classroom lecture setting has failed - a tutor picks up on their interest and relates the subject to the student in a meaningful way. A small class size lets the teacher reach out individually as needed, whereas a large class will miss t

You suddenly realize you got lost in thought and wandered off campus, and are now lecturing to a rutabaga.

Everybody has interests, and math being math almost all interests can be tied back to it if you're halfway clever. If you are completely unable to establish the rapportnecessary to discover those interests for most students, or are unable to link those interests to math, well then perhaps you should reconsider your decision to teach.

That's why a tutor is often able to help these people when a classroom lecture setting has failed - a tutor picks up on their interest and relates the subject to the student in a meaningful way.

That's a really good point. One of the problems with doing real-world examples in a general introductory college math class (ie, calculus, probability and statistics, >25 students) is that many of the subjects one might use require quite a bit of basic knowledge about the field that the example is drawn from.

I don't know. I think the best way to invest in education is to invest in good jobs for parents. When the downward pressure on the lowest 2/3 of the economic scale becomes so great that it breaks up families, causes young people to give up on society, it makes it impossible to have the kind of family structures that create the highest possibility of children entering school with their interests already raised.

By trying to treat the problem at the school-level, we're just medicating the symptom, not dealin

I think you should understand a little bit about vocabulary to understand the problem. "What", you may ask, "does vocabulary have anything to do with math and equations?" Well, first of all, equations are a very specialized form of vocabulary. A lot of formula are symbols which represent concepts. It's no different from a word. The context under which the word is used matters greatly in whether an individual becomes aware of a word which he or she does not understand. The word tectonic could be used to desc

I doubt most mathematicians really understand the Pythagorean Theorem. You get so used to theories and their application that you fool yourself into thinking you know them. Take manual long division or multiplication for example. We understand how to line up the numbers and perform the operations but prove to me that it works or *why* it works! There might be some 45 year old virgin with a severe intellect munching on DMT and living in his mom's basement somewhere in the world who can handle this but I

I think you are confusing mathematicians with engineers. Any mathematician worth his/her salt should know that the Pythagorean Theorem comes straight from the 2-norm in a Euclidean space, which is what most people mean when they say "the distance between two things". You can of course get philosophical and say, "why the 2-norm"?, but this is easily answered by an application of d'Alembert's principle. Now, you see what I did there? Yet another thing to figure out "why is it so", and indeed, you have to work fairly hard to find out how deep the rabbit hole goes.

I doubt most mathematicians really understand the Pythagorean Theorem. You get so used to theories and their application that you fool yourself into thinking you know them. Take manual long division or multiplication for example. We understand how to line up the numbers and perform the operations but prove to me that it works or *why* it works!

I disagree. Some math concepts are deep, but not Pythagoras. Probably the top 5% of high school graduates understand it, and the only reason the majority of the

The probability you are wrong is > 0. If you are writing an article for mathematicians, include equations, If you are writing for non mathematicians then don't use equations. You need to speak in a language that the audience is familiar with.

I'd be happy with complete facts and the whole truth. Equations would bubble up to the surface every once in a while under those conditions. I stopped watching the news (TV) years ago because of the half-truth, spin, and bias on everything--just couldn't trust it anymore and didn't want to waste my time polluting my perception.

"Most people simply do not have the mental capacity to comprehend the meaning of 1 + 1 = 2, and if you do not believe me, go ask the people around you, why 1 + 1 = 2, and not 1 + 1 = 3 ?"

Are you suggesting that we hide maths entirely? Look, there are some things I maybe understand a little, many things I don't understand, and probably an infinite amount of things I don't know about. Just because I don't understand something doesn't mean you should hide the problem from me. If maths is the best way to under

Most of those who have studied advanced math have heard of the Heisenberg's Uncertainty Principle, but not every single one of them understand it

Putting the same Heisenberg's Unvertainty Principle to the "average Joe on the street" and you would most probably get a blank stare

This has nothing to do with elitism, this is about reality

Most people simply do not have the mental capacity to comprehend the meaning of 1 + 1 = 2, and if you do not believe me, go ask the people around you, why 1 + 1 = 2, and not 1 + 1 = 3 ?

Give me a break. In the 1920s Einstein wrote a popular book about special relativity (with formulas) and general relativity for the layman. And we're talking about 2 theories which at the time were at the frontier of physics research. In the last 90 years we haven't suddenly become idiots, so if popular science books talking about special/general relativity and quantum theory (a theory 90 years old !!!!) don't use equations it is because of stupid preconceptions. I've said it before people are not idiots, they may not be specialists in physics research but you can certainly explain them the basics of 2 theories which are almost 1 century old using carefully selected formulas. Nobody goes apeshit if you write Newton's formula of gravitation, why would you go crazy for Heisenberg's uncertaintly principle ?

The cynic in me observes that in this country, every issue is expected to divide into 2 diametrically-opposed sides. Such as, for example, the party that eats their own babies which is the exact opposite of the party that eats everyone else's babies (yes, those are exact opposites and you can only chose one. Snarf).

Furthermore, in adherence to this post-Einstein Weltanschaung that everything should be as simple as possible, then made simpler, everything must be expressed in short sound-bytes suitable for f

Indeed. It's also interesting to note that Einstein's original papers are eminently readable [fourmilab.ch] to the Layman, compared to the kind of papers we see in journals today. Perhaps that's due to the complexity of the mathematics now advanced at the bleeding edge, or perhaps it's because journals try to be even more economical with space than they used to be. I don't know.

Indeed. It's also interesting to note that Einstein's original papers are eminently readable [fourmilab.ch] to the Layman, compared to the kind of papers we see in journals today. Perhaps that's due to the complexity of the mathematics now advanced at the bleeding edge, or perhaps it's because journals try to be even more economical with space than they used to be. I don't know.

Be careful, they seem readable but they're full of subtilities (and in some places even contain errors) especially his 1905 article on the Electrodynamics of Moving Bodies.

And furthermore while they "are" readable to today's audiences because we have almost a century dealing with special relativistic phenomena (it has even entered popular culture) it was not so at the time.Take that into account.

The paper on special relativity is fairly readable. The general relativity paper [wikisource.org] is practically illegible to the layman, requiring tensor mathematics that are usually not taught until the later stages of a physics degree.

He did, however, try to make it more generally accessible, at least to the determined student. This paper is pretty amazing:

If I were to stand outside the universe and observe it then 1+1=2 would prove to be false being that matter is equal to energy. Therefore there is no two of anything--if you really want to be pedantic. It is only a *fact* in our current context of observation.

Without math, it's impossible to convey what you're trying to convey. The press is way too dumbed down already, and many times I've read science stories that are just plain misleading as they try to simplify the message.

Putting equations into news stories means that some people won't understand them, but most importantly it will encourage some of those people to investigate further, and learn how to read equations. If there's no math in the popular press in the first place, then there's no incentive for people to improve themselves.

I agree with this. What I'd like to see is equations added in, where helpful, in the same way as small images in a body of text. Then you could put a caption below, just to say something informal but informative about the equation. I think that way it would be easy for people to decide whether they want to read it. Some people aren't going to want to, so it's important that it's not something you have to read through in the article itself.

Without math, it's impossible to convey what you're trying to convey. The press is way too dumbed down already, and many times I've read science stories that are just plain misleading as they try to simplify the message.

Putting equations into news stories means that some people won't understand them, but most importantly it will encourage some of those people to investigate further, and learn how to read equations. If there's no math in the popular press in the first place, then there's no incentive for people to improve themselves.

no equations doesn't mean no math. Equations generally do a pretty poor job in explaining things. I'd much rather read an article containing "because acceleration is inversely proportional to mass" than one containing "because F=ma"

no equations doesn't mean no math. Equations generally do a pretty poor job in explaining things.

Yes, they do a poor job in explaining things to people who don't know what the terms in the equation mean; raw math often says little if anything, by itself, about the real world, as you have to connect the mathematical items to items in the real world.

But, BTW:

I'd much rather read an article containing "because acceleration is inversely proportional to mass" than one containing "because F=ma"

...I'd rather read an article containing "because, for the same amount of force applied, acceleration is inversely proportional to mass"; my mass is much less than that of a Porsche 911, but I can't even get to 100 km/h on foot or on a bicycle, much

Math is the example you are looking for; where sufficient education has led to the understanding of how to parse a formula and what the terms mean. At that point we can take the mathematical shorthand instead of the description because the audience is presumed to have all the context from previous interaction. Rule of writing #1 say everything your audience needs to understand it and no more. To the original question, equations are shorthand for understanding very complex concepts. Since most readers la

Equations don't do a poor job explaining things. Equations do an excellent job of explaining things...if you have the proper skill to parse them and the educational context to apply them. The problem with using an equation in pop press is that you have to educate the public in the stuff educational context and if you have to go into that detail then you've most likely overridden the benefit of the shorthand mathematical notation.

I think that the equation whiners here overestimate the clarity gained when text does include actual equations. I hate to remind you that probably millions of people have stared at the equation with the deltas and the h-bar, and still managed to completely fail to understand quantum uncertainty. In fact, it's a popular view these days that Heisenberg himself did not understand just what his uncertainty results said about the underlying world. And it's not for a lack of seeing the equation. He derived the da

some people won't understand them, but most importantly it will encourage some of those people to investigate further,

Erm you do know the structure of articles and the state of the readership at large means that "investigate further" in some rare intelligent circumstances where the reader is particularly keen to explore further knowledge, rarely if ever extends to reading to the end of the article.

I don't think anyone at all will read an article and then start on a quest to understand equations within them unless the article is in some obscure field related magazine to the person's work, or they will be graded on their und

Without math, it's impossible to convey what you're trying to convey. The press is way too dumbed down already, and many times I've read science stories that are just plain misleading as they try to simplify the message.

Putting equations into news stories means that some people won't understand them, but most importantly it will encourage some of those people to investigate further, and learn how to read equations. If there's no math in the popular press in the first place, then there's no incentive for people to improve themselves.

Exactly. So what if everyone doesn't get the equations? As long as there is some explanatory context around them, that should be plenty. And some folks might even decide (as mentioned above) to investigate and learn something new.

Mathematics is the only way to accurately describe the universe and everything in it. As such, *everyone* should have a keen interest. Heinlein was a bit tongue-in-cheek, but I think he had it mostly right:Anyone who cannot cope with mathematics is not fully human. At best, h

But they should start with adding footnotes with references first. Most popular science articles don't even mention their sources properly, which sometimes makes it really hard to follow up on them even if you are a scientist.

Willfully ignorant? Not really, no. People have different aptitudes. And there is a far cry between the math taught in schools to the average person, and the math needed to understand Heisenburg and quantum theory.

They should start by using proper units. I know the USA is not metric, so they can use feet, miles and pounds, but football fields, states of delaware and volkswagens are not proper units. (and especially Library of Comgresses)

Personally I think that part of the problem is the non-metric units that are still in use. By accepting that it is in any way sensible to use them, you've already given up on the logical, elegant approach to quantification. You've made it more likely that people resort to the "football fields" etc.

as someone who measures for a living, metric isnt some magical entity that cures all ills. all (real) units have some precise definition, held and maintained by a body or agency of standards, and your vast oversimplification of "everyone different than me" is insulting and itself ignorant of the field of measurement. if the conversion between units scares you, i suggest getting a calculator.

No, not a magic bullet, but a self-consistent, extensible, logical, location-independent basis for straightforward communication. Conversion of units doesn't scare me, it just seems a splendidly archaic and sometimes error-prone way to spend time. A quick trite example: without knowing where your interlocutor lives or works or chooses to base their unit system on, tell me how much liquid is in the gallon container next to my desk?

"Everyone different from me" is amusing, maybe even ironic, though I don't kno

Equations are a great way of explaining something to someone who is familiar with equations. Someone who has done first year undergraduate maths and done reasonably well at it will appreciate having an equation to explain something.

Someone who did fairly poorly at high school maths will look at an equation and say, "What???"

Take Newton's second law. You can explain it in two ways. The first:

When a force is applied to a body, it accelerates in proportion to the force and inverse proportion to its mass.

I've written lots of reports with math formulas (in Latex) where they are needed. Most, if not all, the intended readers have a Ph.D. in experimental physics or optics but I noticed that unless the math is really trivial, they will not follow. Even the slightest math supported reasoning will throw them off. That experience tells me that math for the general audience is probably not a good idea. It is simply pointless the be correct if you are not coming across. Who hears the tree falling in the forest.

You need the explanation to understand what the paper is about. You need the formulas to verify your understanding and to verify the work.

Many people don't read your formulas because they don't have to: they want to get the big ideas, but they aren't interested in verifying your work. For example, your result may be simple enough that they can verify it themselves, or they may decide that it isn't important enough to bother verifying it.

But for your scientific work to be complete, the formulas (or other for

You need the formulas to verify your understanding and to verify the work.

I think that indicates that a lot of people would like to understand the equations, but that they just consider it too much effort.

The thing with a lot of equations is that they are too concise to be easy to understand. I'm going to make a programming analogy here: Looking at any sufficiently sizable and advanced formula is like looking at a sufficiently sizable and advanced regular expression. Sure, if you take the time to carefully examine the regular expression, you will find out what it matches for. It

This is oddly reassuring. I'm a reasonably smart guy, a strong statistician and programmer, and I cannot follow formulas. They're not intuitive and I have to painstakingly work through and translate them as if they were a foreign alphabet. I sometimes wonder whether that's just me, but it seems not. I note that someone in TFA's comments posted a mathematical explanation to demonstrate how much clearer it made things, and at the first Greek letter I skipped to the next comment. No doubt everyone in the

For me this depends on the area. In many parts of CS, you can safely ignore the equations, because they end up being needlessly tedious formalizations of something that was already said in two sentences, and proofs of trivial properties by structural induction. I guess there's a certain "nice to be sure" aspect of restating even straightfoward things with symbols, but rather than having them in the paper, in those cases I'd rather their proofs be formalized in Coq or Isabelle or something and included a che

The general rule regarding the depth of detail in publications should be that they need to be understandable by the target audience. If you write for the general public, then the base text should be layman style, with some pointers where to get more in-depth information for those, who are above the average and more knowledgeable in the specific field. If the target audience is academic and/or scientific community of a specific field, then that's a totally different matter, and the text should be as to-the-point and in-depth as possible, since anyone from the audience would be able to produce superficial treatment of a topic in their field, even if they are not utmost experts of the specific topic, and they'll require exact and deep elaboration of the subject to be able to judge the subtleties, novelties, benefits, etc. I'd say that's all, and it's really not 'rocket science', just spend some time getting to know who'll you'll address with your writing.

The innumeracy of the public is at a lower level than that. This is like arguing about whether kids should be taught calculus in school when they're struggling with basic arithmetic.

What we need is not more equations in the press, but more graphs, tables, and diagrams. I can't count the number of times I've seen a journalist try to explain, say, changing poll results or the interplay between mortgage rates and foreclosures using text, plus a quote from an expert which they clearly don't understand, when a

I think that graphs are often quite misleading. Especially when they are used to show statistical information. You can make very different graphs from same base data. One chooses the graph trying to get best propaganda value.

If someone has an axe to grind, it's easy to make graphs lie. Lying with inferential statistics is a bit more involved, so that gets held off until third year. (No joke, I had a research methods assignment that required me to formulate conclusions then generate a dataset to support them.) But when you legitimately want to understand what's in data, or explain it honestly to someone else, the right visualisation beats statistics every time. Humans are pattern detectors, graphs contain patterns, statistic

Science articles, one would presume, are written for persons interested in science. The idea that there is some broad swath of persons who wish to understand quantum mechanics but stand to be chased off by a simple formula strikes me as unlikely.

If it is a problem, then the logic is the kind of the logic that will perpetuate the problem: the reason math is not as digestible to a public audience is because they're not accustomed to it, and they're not accustomed to it because the media is choosing not to pr

Why reawaken the horrible and traumatic memories of school? Well, unless you were like me who was always good at math. In my case, I would object to news stories containing more references to bullying and teasing. But I've forgiven my childhood bullies of all that. It was easy to do and I've since and I've forgotten most of it. Forgetting it was just as easy as forgetting where I buried their bodies after I took my revenge. *muahahahaha* Ok, I'll take my pills now.

Equations are short hand and full of a form of jargon specific to a field, in terms of the arcane symbols used to represent a property or constant, with the explanation of what each symbol means buried in the text. They are great at condensing meaning, and allowing somebody familiar with them to manipulate them easily. But they are actually terrible at conveying meaning to someone not familiar with the field it is describing.

Often diagrams are the best way to explain mathematical concepts where possible. In the end, most scientist presents with a set of equations or concept to understand, will inevitably spend some time plotting out or trying to pictorially described what it means, to help understand it. So why not short circuit that?

Graphs are very helpful in really conveying what is going on. What we need more in discussions of politics is facts and many facts are about numbers. When discussing who has the right model of the US economy you really need to think of it scientifically. Each model is a hypothesis that needs to be tested. Economics is about aggregate behavior and so it's really a statistical statement. Yes the models are equations and those are nice to show too. But you need to show graphs. Folks who are not innumera

to the name "quantum mechanics" and probably figure that it is a guy who uses a wrench to do something on a car. "Heisenberg" is a guy who cooks blue meth on TV using methyl amine instead of the usual Nazi method.

You want to put math in newspaper articles? That would first require that journalists and editors understand the math. Journalists in the US generally can't differentiate between news and the crap they report on as if it were news (who won on American Idol, etc.).

In "Brief History of Time" Stephen Hawking states that "Someone told me that each equation I included in the book would halve the sales. I therefore resolved not to have any equations at all. In the end, however, I did put in one equation, Einstein's famous equation, E = mc^2. I hope that this will not scare off half of my potential readers."

I do not think the original article was a success for various reasons. It is not easy to explain quantum mechanics convincingly, and I don't think the lack of equations was a main weakness. Those of us who are happy with equations with Hamiltonian operators and eigensolutions probably understand the uncertainty principle too. Those of us who have not touched serious maths, or have done it too long ago will be made to feel stupid rather than being helped.

Most literate people could probably handle arithmetic, fractions, simple exponents, some basic geometry, and linear equations.

However, I would not expect a general-audience article to feature calculus, statistics (beyond references to the mean and median), complex algebra, differentials, etc. As in, everything past pre-algebra class is sketchy, at best.

But algebra beyond linear equations, any kind of complex geometry (beyond rote formulas), calculus, just about anything with a sigma symbol in it, etc. I'm a Computer Engineer, and I don't remember how to do any of that stuff. Format of an equation describing a parabola? Method for computing integrals? How to calculate Standard Deviation? I've forgotten it all; it was 15+ years ago, and has no relevance to my day-to-day life. I could probably pick it up again relatively quickly if I needed to (okay, except for calculus and linear/diffEq; I sucked at it even at the time), but yeah, my eyes would start glazing over any article that relied on my understanding of even moderately complex math.

The first video requires so much previous knowledge to follow. The average person would have no idea what they were saying. And this is "Introductory" to the basics for what is being discussed in the article.

I read the OP's letter, and while it was a great explanation of the actual details of the uncertainty principle by going over what the different variables meant, it didn't enhance my understanding at all. (Not least of all because it left out units.)

It stated the principle, and gave it's exact formula, but didn't tell me why it was true; it said it just was, and that was final. The NYTimes article explained WHY you can't measure both location and velocity simultaneously, and how this does and does not hav

Because if he doesn't cite the math not even the people that know the subject will know if he's right or wrong.

A big problem with "expert opinion" in the press is that they never have to substaniate their opinions. They instead make very vague arguments and say they would get into it further but not in the laypress. Then they fail to follow that up with any further publication in the specialized expert press where all readers could be assumed to understand the subject.

The problem with the original article was that the writer asserted effect for cause:"....Why exactly is the uncertainty principle so misused? No doubt our sensationalist and mystery-mongering culture is partly responsible...."

No, we have a sensationalist and mystery-mongering culture for the same reason we have superstition: fundamental human ignorance, and a failure of the educational system.

It's part of (I believe) a basic function of the human brain to try to organize and explain the environment around

We don't expect journalists to write articles only in Basic English [wikipedia.org]. If someone were to profess that they had never heard of Shakespeare, or didn't know what a metaphor was, we would rightly judge them as being ignorant, or at the least, highly under-educated. Yet, apparently, balking at the simplest of equations is perfectly acceptable.

It's no wonder that we have such shallow thinking, such an abysmal and superficial political discourse, such a disengagement with the notions of science and society, when e

The author struggled to make clear his point and left the impression he was creating a strawman argument

Strange - I found his arguments (in the first article, didn't read the second) quite straight forward, and I feel that adding equations would only have obfuscated matters. Most people don't understand equations and inequalities or their specific significance, and that goes for a lot of well-educated people too. The significance of Heisenberg's inequality is that you can use it in quantitative calculations when you test your theory, but it does not in itself add much to your intuitive understanding of the pr

1) You use no math. This conveys no information to those who might actually take something away from an article, while giving the masses a fluff piece which at best make them think they know something about the topic.

2) You use math. Now you can convey something meaningful to some part of the audience. You'll turn off some people too, but at least they'll realize they don't actually understand it.

A good book to read on this topic is David Bodanis's E=mc^2,"A biography of the world's most famous equation"

It's not just another Einstein book. It's actually about just the equation and its life.The author gives examples of how printing houses using different equation notation were like Microsoft, driving out the competition for the standard.All manner of symbols were used for math, some examples:

"The author notes that an editor warned him that for every equation in the book the readership would be halved, hence it includes only a single equation: E = mc2. Early in 1983, Hawking approached Simon Mitton, the editor in charge of astronomy books at Cambridge University Press, with his ideas for a popular book on cosmology. Mitton was doubtful about all the equations in the draft manuscript, which he felt would put off the buyers in airport bookshops that Hawking wished to reach. It was with some difficulty that he persuaded Hawking to drop all but one equation.[4] In addition to Hawking's notable abstention from presenting equations, the book also simplifies matters by means of illustrations throughout the text, depicting complex models and diagrams." https://en.wikipedia.org/wiki/A_Brief_History_of_Time [wikipedia.org] it may not be true as after all the book sold rather well.

This is what I came here to say, too. The "no-equations" dictum is pretty much an ironclad rule from editors and publishers. The author in question basically has no say in the matter. Which is pretty messed up, in that everyone is required to take basic algebra to communicate in that language, and then it's banned by fiat from our popular media.

Come to think of it, if the tendency for PR firms to arrange for an "equation for the best sandwich" [google.co.uk] etc. suggests that an equation is actually quite an easy way of getting the public's attention.

One should bother because pandering to the lowest denominator will ensure that most will meet that expectation.There is a range of happy media between a wall of mathematical formulae and proofs and an awkwardly written, purely textual interpretation. Not everyone will have a full (or even good) comprehension of the meaning, but those willing to be challenged will have something on which to proceed.Those who don't care or who like pap can just move on to the latest on Kate and William (who, I believe, just

You can write about the results - which is important - but you can't write about the mechanics without at least describing the mathematical concepts and their relations with physical reality. This is why it's such a problem, because everyone deduces from the results written up in the newspapers how they think the mechanics work, and of course they get it wrong because it's profoundly unintuitive.

And at least in this particular case, "no" is indeed the correct answer. Equations can never be a substitute for actual understanding. You can use equations to develop understanding by starting from an earlier point and transform the initial equation to establish a new fact. But where do you start with quantum mechanics? "Quantum states are being represented by rays in a complex Hilbert space"?

If anything, equations can be used to create an argumentum ad auctoritatem, and I'm not sure that this is a good thing.

In most contexts this is too true, and quite sad. However, if you aren't allowed to tell a story "according to quantum mechanics", you have no chance of explaining the functioning of the ordinary objects all around us, like lasers, LEDs, microwave ovens, fucking magnets, superconductors, sunshine, and many others. The real problem is that "according to quantum mechanics" has been so abused that people reflexively glaze over when they hear it. That abuse has made the world stupider and sadder, and undoing th

I don't know where you lived before moving to Thailand, but I want to go there. Here in the US, I have a difficult time finding people with an IQ over 110. Oh sure, there are colleges and R&D firms with plenty of bright people but step outside and find there is nothing but morons as far as the eye can see.